[math-fun] orrery problem

My brother is interested in building an orrery, and posed the following (somewhat ill-defined) problem: given a bag of gears and a set of periods, how do you partition them to get the best set of gear chains? Continued fractions, of course, give the best rational approximations to a given period, but that assumes you can choose the number of teeth. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com